Aren't there definitions of Truth that are not the negation of Falsehood? Can't there be a function True(x) that is not equal to !False(x)? Can't there be a third function Paradox(x) such that these counterexamples can be considered paradoxes and therefore outside of the truth?

I'm admittedly not a logician and don't formally study paradoxes, but I never quite understood the whole category of "this sentence is false" paradoxes, I feel that the sentence is paradox and therefore it's neither false nor true.

I do agree that it's a truth vector sounds like a silly panacea fantasy, though. But more logical formality is not the counter argument that would convince me of it, rather I believe that there's less formal and rigorous ways to get closer to truth.

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galaxyLogic 5 hours ago | parent | next [-]

Interesting point about "self-referential sentences". I tend to agree. In my view a sentence saying something like "This sentence ..." does not have valid semantic meaning. It says nothing because, what "This" in "This sentence" means is ill-defined.

If terms we use are not well-defined, then sentences using such terms can not have meaning.

But for the sake of argument let's explore, what could the "this" in (so called) "self-referential" sentences refer to?

Do they refer to a specific encoding of the sentence you are reading, as some bits in computer memory perhaps?

That would require that those bits somehow have a unique "identity" and the "this" in a self-referential sentence would have to refer to those bits in specific addresses of a specific memory-chip.

But of course the "this" does not specify which memory chip, which specific (concrete) encoding of its (purported) meaning it is referring to. And if it did, then it would be talking about that specific set of bits in that specific memory-chip, not of "itself".

The fallacy is that what we perceive as a "sentence we read" is somehow "speaking" of something. But no, the sentence is not a subject, a sentence can not speak, and THEREFORE it specifically can not speak of itself.

A sentence can not speak, only actors, only subjects, like humans and AI, can "speak". And their speech must be encoded in some physical medium. A written sentence like "This sentence is ..." gives us the false impressions that somehow the SENTENCE IS SPEAKING of itself!

But speech can not speak, speech is the product of speaking.

Hence, in my view, "self-referential sentences" do not have any meaning and whatever paradoxes they might seem to create are results of confusion between ontological levels of "Subject" vs. "Speech".

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aesthesia 2 hours ago | parent | next [-]

Quines produce similar issues to self-referential sentences without being directly self-referential. e.g. "'Yields falsehood when preceded by its quotation' yields falsehood when preceded by its quotation."

	▲	TZubiri 2 hours ago \| parent [-]
		> "'Yields falsehood when preceded by its quotation' yields falsehood when preceded by its quotation." Here be the limits of my brain. It does feel (vibes) like an obfuscation of the self-referential canonical 'This sentence is false' example, like a sum of obfuscation techniques that are designed to confuse, but don't materially change the nature of the phenomenon: 1- reference is made implicit, instead of explicit 2- References another object, necessitating (at least) two instances of the same sentence, with one referencing the other. 3- Maybe some unnecessarily complex language that could be made simpler? So what I'm getting out of it is that it feels like a mental trap that is hard to compute and understand because it was designed that way (or because it evolved that way), not necessarily because of it containing a fundamentally useful knowledge, it's difficulty to parse IS itself the interesting property of the sentence. Maybe meta analysis like looking into the history of this sentence and seeing how many people went crazy going down that rabbit hole would be more enlightening than engaging in it in good faith. Which might only be useful if you have a high enough IQ that it doesn't confuse you any longer.

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erehweb 3 hours ago | parent | prev [-]

As the article notes, the sentence "This sentence is written in English" is well understood, and true. "This sentence is written in French" is also well understood and false.

	▲	TZubiri 2 hours ago \| parent [-]
		Right, my original comment wasn't about self-reference, but paradoxes, and not all self-references result in paradoxes. Not sure what the difference between the language of a sentence and the truthiness of a sentence is. Maybe it has to do with the fact that the language refers to syntactical features that can be determined at 'compile' time, while truthiness refers to a semantic quality feature that can only be determined at 'runtime'. (See en.wikipedia.org/wiki/colorless_green_ideas_sleep_furiously for at the very least a funny canonical example of a syntactically valid, but semantically nonsensical sentence.) The fact that the language function can also be mapped to reduced parts of the sentence, might also be relevant, you can deduce that "This-" and "This sentence is-" are English, while you cannot partially compute that "This sentence is-" is true. A single negation bit being enough to change the result of the operation.

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codechicago277 4 hours ago | parent | prev | next [-]

I’m not a logician either but believe this is what Tarski’s definition of truth solves for. In order to make a statement about the statement itself, you have to introduce a new meta language. Then a statement in the meta language is only true if the underlying statement is true.

Much more rigorous explanation: https://plato.stanford.edu/entries/tarski-truth/

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roywiggins 5 hours ago | parent | prev | next [-]

There is no lack of more elaborate logics:

https://en.wikipedia.org/wiki/Non-classical_logic

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UltraSane 5 hours ago | parent | prev | next [-]

There are a LOT of different logical system.

Paraconsistent Logic

Intuitionistic Logic

Dialetheism

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cgio 4 hours ago | parent | prev [-]

Fuzzy logic?